Identifying a hierarchy of learning about percentages

Joan Martina Burfitt

Research output: ThesisMaster's Thesis

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[Truncated] The development of understandings in using and interpreting percentages is essential to meet the mathematical demands in the personal and working lives of most Australian citizens. Individuals can have a greater appreciation of data and make more informed decisions when they have an understanding of the relative size of fractional components and they can compare proportional amounts: a sound understanding of percentages facilitates this understanding.
Percentages have been shown to be a difficult topic for teachers to teach and students to learn and the performance of Australian students can be much improved. Information that could support teachers in their planning of learning programs and that could inform their teaching of this important topic could result in better outcomes for students and society. Higher skills development could lead to greater achievement in higher level mathematics and better job prospects for more young Australians.
A review of the research literature indicated that, although some skills appear to be mastered before others, no specific hierarchy for learning about percentages had been described. The purpose of this study was to research the possibility of constructing a developmental scale for describing this hierarchy and to identify its features.
Based on the literature review, a hierarchical, developmental pathway for learning was proposed. For this hierarchy, skills were classed into different aspects including the use of models to represent percentages, knowing fraction equivalents, understanding key concepts about percentages and the determination of percentage change.
An assessment instrument to test students’ skills, knowledge and understanding of percentages according to the proposed hierarchy of learning was constructed and piloted before being refined and used with secondary students in Years 7-10 in Western Australian Catholic Schools. About 500 students completed the final version of the test online and because of the explicit relative difficulties of item parameter estimates, Rasch measurement theory was applied to their responses. The students and their teachers were invited to respond to a short survey on content features of the test questions and the test administration.
Original languageEnglish
Awarding Institution
  • The University of Western Australia
Publication statusUnpublished - 2014


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